Supporters of the proposal say it's a common-sense way to keep guns away from potentially dangerous people without encroaching on Second Amendment rights.

"While no one law or set of laws can end gun violence, by taking these steps — and requiring background checks on all commercial gun sales — we can make our communities safer and prevent more shootings while respecting the rights of law-abiding gun owners," Thompson said.

The legislation arrives one week after a shooting and stabbing spree in Santa Barbara, Calif., left seven people dead, including the gunman. Police say Elliot Rodger, a 22-year-old former Santa Barbara City College student, fatally stabbed three men in his apartment, then shot and killed three others before taking his own life with a handgun.

Rodger had a history of mental illness, and his family had alerted police about suspicious behavior in the month before the violence occurred.

The authorities visited Rodger at home, but determined "he did not meet the criteria for an involuntary hold,” according to Santa Barbara County Sheriff Bill Brown.

The House on Thursday passed bipartisan legislation increasing funding for an FBI database designed to block gun sales to certain criminals and the severely mentally ill. The Thompson-Perlmutter bill, supporters say, would complement that effort.

"This young man's family reached out for support and did not find the support there," Rep. Elizabeth Esty (D-Conn.), said of Rodger. "It is our duty, as members of Congress, to ensure that families, law enforcement [and] mental health professionals have the support they need to keep us safe."

The Democrats' bill would expand the federal prohibition on gun sales to include those convicted of misdemeanor stalking, as well as those receiving involuntary mental health services on an outpatient basis, if a court deems them dangerous. The current ban applies largely to those committed on an inpatient basis.

The proposal would also provide states grant money to help local authorities bolster gun-violence prevention programs. One such effort, the Democrats suggest, would be to empower police to seek warrants to seize firearms from those they believe might use them to harm themselves or others.

The bill has little chance of moving through the Republican-led House, where GOP leaders have refused all calls to consider tougher gun laws in recent years. Still, House Minority Leader Nancy Pelosi (D-Calif.) on Thursday urged Congress to pass the measure "without delay."

"As more details emerge about the Santa Barbara shooter, it's clear that we must keep guns away from those at risk of hurting themselves or hurting others," she said.

It's unclear if the bill’s measures could have prevented the recent Santa Barbara shooting — something even the Democrats acknowledge.

But that, Thompson said Friday, "is no excuse not to try to do what we can do."